Question

Find the slant asymptote x^2+7x-7/x-2

Answer 1

To find the slant asymptote of the rational function (x^2+7x-7)/(x-2), we need to divide the numerator (x^2+7x-7) by the denominator (x-2) using long division or synthetic division.

Using long division:

x + 9
___________________
x - 2 | x^2 + 7x - 7
- (x^2 - 2x)
__________
9x - 7
- (9x - 18)
___________
11

The quotient is x + 9, and the remainder is 11.

Therefore, the slant asymptote is given by the equation y = x + 9.

Note: The degrees of the numerator and denominator are the same (both are 1), so there is no horizontal asymptote. Instead, there is a slant asymptote.